Subaperture polishing techniques are useful for preventing difficulties associated with using polishing pads of roughly the same size as a sample being polished. For example, there can be edge effects resulting from the pad making contact with the edges. This can create “pad rebound”, wherein the pad repeatedly bounces off of the sample, or “burn off,” wherein the contact area with the pad is disproportionately small so that too much material is worn away. The use of subaperture techniques, using a pad smaller than the sample that is swept from an edge to a middle region of the sample, can reduce or even eliminate some of these drawbacks. Conventional systems use a uniform polishing rate to produce uniform profiles for flat surfaces. In cases, where non-uniform profiles are desired, the sample and one or more polishing heads may be moved relative to one another to differentially polish different areas of the sample.